Final Project

Read in the data for Final Project

raw_data = read.table("nba_scores.csv",sep = ",",header = TRUE)
elo_initials = read.table("nba_initial_elos.csv",sep = ",",header = TRUE)

HFA & Weight Calclulation for 21st century

year_list = c(2000,2001,2002,2003,2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015,2016,2017,2018,2019,2020)
# list for saving hfa and weight in different years
hfa_list = c()
weight_list = c()
for (x in year_list){
  home_wins = 0
  games = 0
  first_game_index = 1
  scores = raw_data[which(raw_data$season==x),] 
  # Iterate through games - first index can be changed to eliminate early seasons where scores are extreme
  for(i in first_game_index:nrow(scores)) {  
    # Count number of games that do not end in ties
    if(scores$home_score[i] != scores$away_score[i]) { games = games + 1 }
    
    # Count number of games where home team wins
    if(scores$home_score[i] > scores$away_score[i]) { home_wins = home_wins + 1 }
  }
  
  home_win_prob = home_wins / games  # Calculate home win probability where outcome was not a tie
  hfa = -400*log10(1/home_win_prob - 1)  # Calculate number of Elo points added to home team
  hfa_list <- append(hfa_list,hfa)
  
  starting_weight = 0  # Lower bound for weight ranges to be tested - generally set equal to 0
  iterations = 100  # Number of k values to test
  step_size = 0.1  # Amount to increment k by at each step
  first_game_index = 1
  
  # Initialize data frame to store k values and corresponding error
  errors = data.frame(matrix(ncol = 2, nrow = iterations))
  colnames(errors) = c("weight", "error")
  errors$weight = starting_weight + (1:iterations)*step_size
  errors$error = NA
  
  # Iterate through all potential k values that are being tested
  for(counter in 1:iterations) {
    weight = starting_weight + counter*step_size  # Calculate k value for current iteration
    error = 0  # Reset error for current iteration
    elos = read.table("nba_initial_elos.csv", header=TRUE, sep=",")  # Reset initial Elo ratings
    
    # Iterate through games - first index can be changed to eliminate early seasons in a league where early results tend to be extreme
    for(i in first_game_index:nrow(scores)) {  
      # Find indices corresponding to home and away teams for current game
      home_index = which(elos$team == scores$home_team[i])
      away_index = which(elos$team == scores$away_team[i])
      
      # Find home and away team Elo ratings
      home_elo = elos$rating[home_index]
      away_elo = elos$rating[away_index]
  
      # Calculate home team win probability
      win_prob = 1 / (10^((away_elo - (home_elo + hfa*scores$neutral[i]))/400) + 1)
      
      # Calculate actual margin of victory - must be positive
      score_diff = abs(scores$home_score[i] - scores$away_score[i])  
    
      # Determine home team result
      if(scores$home_score[i] > scores$away_score[i]) { 
        home_result = 1  # Home team wins
      } else if(scores$home_score[i] < scores$away_score[i]) { 
        home_result = 0  # Home team loses
      } else { 
        home_result = 0.5  # Tie
      }
      
      # Add squared error between home result and predicted probability of home team winning to SSE
      error = error + (home_result - win_prob)^2
      
      # Calculate amount each team's Elo rating is adjusted by
      home_elo_adjustment = weight * log(score_diff + 1) * (home_result - win_prob)
    
      # Adjust Elo ratings - add point to winner and subtract points from loser
      elos$rating[home_index] = elos$rating[home_index] + home_elo_adjustment
      elos$rating[away_index] = elos$rating[away_index] - home_elo_adjustment
  
      # Adjust Elo ratings at end of season to regress 1/3 of the way towards 1500
      if(i < nrow(scores) && scores$season[i+1] > scores$season[i]) {
        for(j in 1:nrow(elos)) {
          if(scores$season[i] >= elos$inaugural_season[j]) {
            elos$rating[j] = elos$rating[j] - (elos$rating[j] - 1500)/3
          }
        }
      
        existing_teams = elos[which(elos$inaugural_season <= (scores$season[i] + 1)),]
        expansion_adjustment = -1*(mean(existing_teams$rating) - 1500)
      
        for(j in 1:nrow(elos)) {
          if((scores$season[i] + 1) >= elos$inaugural_season[j]) {
            elos$rating[j] = elos$rating[j] + expansion_adjustment
          }
        }
      }
    }
    errors$error[counter] = error  # Store error for current iteration
  }
  
  # Choose and print optimal weight based on value that had the lowest SSE
  weight = errors$weight[which(errors$error == min(errors$error))]
  weight_list <- append(weight_list,weight)
}

print(hfa_list)

##  [1] 68.14165 64.13962 90.41023 85.61199 71.86992 76.27353 66.90464 77.83927
##  [9] 79.29028 69.77472 76.19808 65.46320 80.18853 55.52015 53.14886 66.26620
## [17] 58.13276 60.99658 63.73097 32.62010 32.43418

print(weight_list)

##  [1] 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0
## [16] 10.0  9.9 10.0 10.0 10.0 10.0

SAVE weight and hfa into csv fie(The calculation takes long time so save it into csv file for later use)

write.table(as.data.frame(hfa_list),file="hfa.csv", quote=F,sep=",",row.names=F)
write.table(as.data.frame(weight_list),file="weight.csv", quote=F,sep=",",row.names=F)

Read HFA and wight data from csv;

hfa_list=read.csv("hfa.csv")
weight_list=read.csv("weight.csv")

Set up

#Only use data from 2000 to 2020
scores = raw_data[which(raw_data$season > 1999),]
#Get all the team name
team_name=unique(scores$home_team)
#Combine hfa and weight into dataframe
Adjustment<-cbind(hfa_list,weight_list)

Elo Ratings Calclulation for 21st century

# Use list to store average elo ratings for each year from 2000 to 2020
stack=list()
for(teamN in team_name){
  
  

inital_year=2000


# Optimal weight from code above. If the above code is run first, the line below can be commented out. Otherwise, you can type the optimal k-value below without needing to run the chunk of code above.
for(i in 1:nrow(Adjustment)){
  


weight = Adjustment[i,"weight_list"]
hfa =Adjustment[i,"hfa_list"]

# Select team and season to follow for a period of time
team = teamN
first_season = inital_year
last_season = inital_year

inital_year=inital_year+1

# Read in initial team Elo ratings and history of games
elos = read.table("nba_initial_elos.csv", header=TRUE, sep=",")
scores =raw_data[which(raw_data$season<=first_season),] 

# Create data frame to store information for team specified above
team_results = data.frame(matrix(ncol = 8, nrow = 0))
colnames(team_results) = c("opponent", "pregame_elo", "win_probability", "result", "team_score", "opponent_score", "elo_adjustment", "postgame_elo")

# Iterate through all games in the sport's history
for(i in 1:nrow(scores)) {
  # Find indices corresponding to home and away teams for current game
  home_index = which(elos$team == scores$home_team[i])
  away_index = which(elos$team == scores$away_team[i])
  
  # Find home and away team Elo ratings
  home_elo = elos$rating[home_index]
  away_elo = elos$rating[away_index]

  # Calculate home team win probability
  win_prob = 1 / (10^((away_elo - (home_elo + hfa*scores$neutral[i]))/400) + 1)

  # Calculate actual margin of victory - must be positive
  score_diff = abs(scores$home_score[i] - scores$away_score[i])   
  
  # Determine home team result
  if(scores$home_score[i] > scores$away_score[i]) { 
    home_result = 1  # Home team wins
  } else if(scores$home_score[i] < scores$away_score[i]) { 
    home_result = 0  # Home team loses
  } else { 
    home_result = 0.5  # Tie
  }
  
  # Calculate amount each team's Elo rating is adjusted by
  home_elo_adjustment = weight * log(score_diff + 1) * (home_result - win_prob)
  
  # Adjust Elo ratings - add point to winner and subtract points from loser
  elos$rating[home_index] = elos$rating[home_index] + home_elo_adjustment
  elos$rating[away_index] = elos$rating[away_index] - home_elo_adjustment
  
  # Add game information to team result data frame for each team game of the team specified above if team and season both match
  if(scores$season[i] >= first_season & scores$season[i] <= last_season & (scores$home_team[i] == team | scores$away_team[i] == team)) {
    if(scores$home_team[i] == team) {  # If specified team was at home
      team_results[nrow(team_results) + 1,] = c(scores$away_team[i], elos$rating[home_index] - home_elo_adjustment, win_prob, home_result, scores$home_score[i], scores$away_score[i], home_elo_adjustment, elos$rating[home_index])
    } else {  # If specified team was away
      team_results[nrow(team_results) + 1,] = c(scores$home_team[i], elos$rating[away_index] + home_elo_adjustment, 1-win_prob, 1-home_result, scores$away_score[i], scores$home_score[i], -1*home_elo_adjustment, elos$rating[away_index])
    }
  }
  
  # Adjust Elo ratings at end of season to regress 1/3 of the way towards 1500
  if(i < nrow(scores) && scores$season[i+1] > scores$season[i]) {  # New season
    for(j in 1:nrow(elos)) {  # For each team
      if(scores$season[i] >= elos$inaugural_season[j]) {  # Check if team existed
        # Move each team's Elo rating back towards 1500 by 1/3 of the difference
        elos$rating[j] = elos$rating[j] - (elos$rating[j] - 1500)/3
      }
    }
    
    # Identify all teams that existed at beginning of following season
    existing_teams = elos[which(elos$inaugural_season <= (scores$season[i] + 1)),]
    
    # Calculate amount each team's Elo rating must be adjusted by to make mean 1500
    expansion_adjustment = -1*(mean(existing_teams$rating) - 1500)
    
    # Perform expansion adjustment on teams that existed at beginning of following season
    for(j in 1:nrow(elos)) {  # For each team
      if((scores$season[i] + 1) >= elos$inaugural_season[j]) {  # Check if team existed
        elos$rating[j] = elos$rating[j] + expansion_adjustment  # Update ratings if so
      }
    }
  }
}
# Change data type to numeric
temp=transform(team_results,postgame_elo=as.numeric(postgame_elo))
# Store the elo into the list
stack=append(stack,mean(temp$postgame_elo))





}




}

Clean elo rating for each team and store everything in to df

# Create a dataframe that contains teams' name and their elo rating for each year
df=data.frame(matrix(ncol=30,nrow=21))
colnames(df)=team_name
team_number=1
row=1
for(i in 1:length(stack)){
  df[row,team_number]=stack[i]
  row=row+1
  if(i%%21==0){
    team_number=team_number+1
    row=1
  }
 
}
## Remove nan value in the elo rating
## Since these nan values are caused by no games or team reorganize so we initial it as the initial elo ratings
df[1,30]=1400
df[2,30]=1400
df[3,"Charlotte Hornets"]=1400
df[4,"Charlotte Hornets"]=1400

df

##    Orlando Magic Atlanta Hawks Brooklyn Nets Toronto Raptors New York Knicks
## 1       1512.578      1348.977      1382.767        1529.481        1552.360
## 2       1519.962      1385.598      1537.059        1520.403        1438.110
## 3       1502.088      1414.345      1601.256        1383.043        1430.943
## 4       1362.400      1388.205      1578.669        1396.073        1455.673
## 5       1420.943      1287.624      1465.098        1420.775        1435.460
## 6       1408.274      1297.400      1550.400        1395.466        1353.064
## 7       1487.848      1379.312      1504.171        1480.783        1393.329
## 8       1574.085      1435.444      1438.920        1530.162        1349.833
## 9       1660.072      1531.681      1434.610        1441.936        1393.674
## 10      1671.369      1592.194      1282.836        1470.645        1388.507
## 11      1642.035      1547.372      1329.773        1366.798        1476.039
## 12      1567.552      1540.793      1332.073        1357.368        1492.788
## 13      1361.786      1530.214      1493.860        1413.401        1593.159
## 14      1320.602      1477.171      1502.553        1540.488        1471.181
## 15      1330.203      1625.417      1461.463        1573.115        1342.797
## 16      1420.435      1566.538      1359.656        1593.502        1386.316
## 17      1394.437      1512.875      1294.377        1594.329        1415.081
## 18      1369.359      1379.129      1373.786        1644.333        1414.033
## 19      1444.077      1348.934      1452.529        1655.317        1307.248
## 20      1486.428      1355.032      1473.297        1679.725        1311.988
## 21      1392.213      1505.946      1578.862        1528.453        1483.369
##    Dallas Mavericks Houston Rockets San Antonio Spurs Chicago Bulls Utah Jazz
## 1          1591.778        1537.814          1675.189      1248.654  1619.731
## 2          1635.241        1456.316          1671.600      1281.701  1558.476
## 3          1704.404        1504.038          1681.439      1352.033  1560.562
## 4          1621.615        1561.089          1695.795      1346.120  1505.034
## 5          1638.867        1567.068          1722.777      1461.916  1425.894
## 6          1692.314        1505.854          1702.870      1498.784  1440.638
## 7          1714.482        1573.407          1687.105      1568.286  1581.448
## 8          1628.145        1606.177          1668.317      1473.430  1623.492
## 9          1570.834        1621.814          1624.047      1471.621  1596.866
## 10         1603.383        1560.179          1595.411      1488.580  1602.854
## 11         1650.893        1505.318          1672.686      1629.686  1532.371
## 12         1605.043        1520.907          1662.311      1675.369  1493.342
## 13         1499.577        1545.655          1700.623      1560.450  1519.892
## 14         1569.809        1613.511          1703.097      1528.041  1411.149
## 15         1598.562        1634.076          1675.839      1568.128  1429.687
## 16         1530.417        1533.151          1748.373      1511.650  1515.781
## 17         1441.790        1605.544          1707.823      1483.867  1578.967
## 18         1409.193        1698.182          1588.077      1406.540  1568.108
## 19         1431.524        1630.326          1548.938      1318.918  1596.887
## 20         1550.709        1618.926          1495.799      1359.948  1593.988
## 21         1544.804        1397.140          1502.575      1426.581  1646.461
##    Portland Trailblazers Golden State Warriors Memphis Grizzlies
## 1               1642.740              1312.091          1362.745
## 2               1570.541              1320.778          1329.445
## 3               1599.260              1428.947          1372.699
## 4               1514.750              1468.902          1537.364
## 5               1441.475              1422.575          1556.248
## 6               1345.612              1473.983          1560.822
## 7               1374.908              1486.709          1406.928
## 8               1475.123              1581.835          1355.412
## 9               1566.178              1443.175          1322.824
## 10              1583.983              1381.520          1458.657
## 11              1552.494              1428.487          1527.733
## 12              1523.934              1451.575          1579.043
## 13              1450.839              1514.690          1633.213
## 14              1578.012              1599.087          1576.986
## 15              1617.572              1729.056          1631.497
## 16              1536.882              1819.362          1532.061
## 17              1522.617              1776.272          1513.912
## 18              1560.228              1720.183          1402.190
## 19              1607.011              1678.043          1417.907
## 20              1511.423              1420.175          1451.602
## 21              1525.967              1463.331          1527.203
##    Philadelphia 76ers Boston Celtics Cleveland Cavaliers Charlotte Hornets
## 1            1626.664       1445.540            1413.022          1579.744
## 2            1544.190       1534.978            1384.473          1534.144
## 3            1552.466       1532.924            1296.688          1400.000
## 4            1465.920       1446.751            1373.631          1400.000
## 5            1456.548       1491.084            1500.606          1369.137
## 6            1469.158       1466.464            1547.565          1346.137
## 7            1418.231       1377.199            1575.397          1398.292
## 8            1477.296       1653.579            1539.650          1412.513
## 9            1500.772       1710.315            1696.196          1438.418
## 10           1416.064       1628.131            1725.939          1509.773
## 11           1481.746       1663.776            1376.380          1450.106
## 12           1547.014       1577.060            1361.565          1276.994
## 13           1447.657       1529.151            1339.011          1244.856
## 14           1306.377       1404.732            1375.072          1428.789
## 15           1266.877       1414.549            1568.167          1449.779
## 16           1231.525       1552.119            1672.535          1504.589
## 17           1320.339       1583.494            1645.776          1511.207
## 18           1524.922       1609.203            1580.703          1465.218
## 19           1597.386       1589.661            1363.455          1481.095
## 20           1588.602       1643.199            1322.577          1401.040
## 21           1597.592       1555.697            1360.845          1452.479
##    Miami Heat Oklahoma City Thunder Los Angeles Lakers Denver Nuggets
## 1    1580.383              1516.280           1660.021       1466.015
## 2    1451.793              1565.449           1712.430       1401.871
## 3    1403.929              1516.953           1612.539       1316.763
## 4    1446.529              1490.728           1640.088       1473.772
## 5    1642.723              1591.700           1522.708       1526.876
## 6    1622.909              1460.803           1511.214       1537.941
## 7    1532.870              1450.857           1537.886       1520.907
## 8    1333.792              1338.357           1638.245       1573.056
## 9    1447.051              1306.026           1739.274       1611.590
## 10   1521.518              1530.456           1691.358       1628.885
## 11   1660.722              1607.454           1663.049       1587.122
## 12   1683.304              1685.590           1596.489       1574.166
## 13   1715.831              1701.643           1531.048       1622.817
## 14   1672.894              1687.167           1413.574       1511.743
## 15   1495.546              1578.792           1353.524       1438.651
## 16   1531.055              1645.570           1281.701       1423.737
## 17   1499.393              1594.343           1351.878       1471.559
## 18   1521.597              1553.924           1419.346       1534.241
## 19   1478.437              1586.461           1481.179       1601.815
## 20   1580.975              1571.687           1636.367       1598.682
## 21   1537.013              1425.462           1619.727       1602.220
##    Phoenix Suns Los Angeles Clippers Washington Wizards Detroit Pistons
## 1      1595.597             1346.182           1342.800        1442.917
## 2      1519.109             1498.220           1421.632        1527.419
## 3      1522.861             1414.939           1459.551        1588.445
## 4      1433.860             1414.790           1367.160        1620.196
## 5      1641.622             1451.457           1474.865        1627.845
## 6      1657.980             1544.845           1496.490        1713.694
## 7      1674.107             1509.988           1519.611        1628.539
## 8      1647.815             1411.232           1482.104        1660.406
## 9      1561.894             1312.553           1348.677        1539.739
## 10     1598.623             1363.242           1353.936        1387.911
## 11     1544.909             1377.159           1320.537        1379.259
## 12     1504.812             1536.857           1309.898        1377.531
## 13     1422.806             1629.449           1383.476        1396.885
## 14     1515.269             1648.869           1501.079        1397.924
## 15     1544.841             1653.669           1543.050        1387.393
## 16     1382.318             1625.293           1493.885        1498.609
## 17     1343.418             1607.481           1545.416        1483.242
## 18     1324.254             1535.641           1541.475        1471.678
## 19     1280.644             1537.639           1447.112        1483.617
## 20     1412.429             1618.544           1396.223        1409.682
## 21     1628.820             1632.801           1412.243        1361.860
##    Indiana Pacers Minnesota Timberwolves Milwaukee Bucks Sacramento Kings
## 1        1525.005               1559.074        1573.391         1627.307
## 2        1496.920               1601.366        1555.892         1677.376
## 3        1552.680               1568.133        1482.015         1670.818
## 4        1622.613               1644.186        1503.928         1659.236
## 5        1551.911               1558.584        1435.059         1595.298
## 6        1535.426               1498.267        1444.227         1514.539
## 7        1469.696               1447.527        1421.174         1482.851
## 8        1429.621               1319.242        1368.186         1450.946
## 9        1451.712               1351.452        1414.023         1346.882
## 10       1415.962               1291.827        1497.597         1341.896
## 11       1467.955               1296.799        1477.586         1319.888
## 12       1550.653               1411.930        1480.390         1387.802
## 13       1584.230               1421.391        1475.542         1377.870
## 14       1623.789               1523.177        1301.804         1398.588
## 15       1476.973               1348.713        1437.570         1411.745
## 16       1532.926               1339.507        1424.681         1425.552
## 17       1502.295               1430.135        1470.314         1415.515
## 18       1529.064               1530.215        1509.227         1348.429
## 19       1577.161               1500.547        1661.946         1456.291
## 20       1554.705               1413.028        1713.567         1445.720
## 21       1502.121               1334.271        1622.999         1440.451
##    New Orleans Pelicans
## 1              1400.000
## 2              1400.000
## 3              1489.062
## 4              1509.359
## 5              1356.579
## 6              1441.606
## 7              1459.113
## 8              1604.971
## 9              1596.136
## 10             1476.641
## 11             1526.021
## 12             1408.431
## 13             1407.933
## 14             1431.714
## 15             1495.990
## 16             1448.355
## 17             1417.812
## 18             1528.619
## 19             1511.747
## 20             1454.883
## 21             1486.189

Save elo into csv file

write.csv(df,"elo.csv",row.names = FALSE)

import elo data

df=read.csv("elo.csv")

Analysize data store mean, median and sd in the list

# List for storing mean,median,and sd
mean_stack=list()
sd_stack=list()
median_stack=list()

# Calculate mean, median,and sd
for(i in colnames(df)){
  mean_stack=append(mean_stack,mean(df[,i]))
  sd_stack=append(sd_stack,sd(df[,i]))
  median_stack=append(median_stack,median(df[,i]))
  
  
}

Get Descriptive Statistics and store them in the descriptive dataframe

# Store everything in the descriptive_stat dataframe
mean_df=as.data.frame(do.call(rbind,mean_stack))
colnames(mean_df)="mean"
sd_df=as.data.frame(do.call(rbind,sd_stack))
colnames(sd_df)="sd"
median_df=as.data.frame(do.call(rbind,median_stack))
colnames(median_df)="median"
descriptive_stat=cbind(colnames(df),mean_df,sd_df,median_df)
colnames(descriptive_stat)=c("team","mean","sd","median")

store the Descriptive Statistics

write.csv(descriptive_stat,"descriptive.csv",row.names = FALSE)

import Descriptive Statistics

descriptive_stat=read.csv("descriptive.csv")

# Reset the team name since the names have some changes
team_name=colnames(df)

Create plot of Elo ratings for different team from 2000-2020

library(ggplot2)

df$year=2000:2020
#Create plot of Elo ratings for different team from 2000-2020
for(i in team_name){

 plot.ts(df[,i],xlab = "Year from 2000 to 2020",  ylab = "Elo Rating",main = paste("Team: ",i))
  #axis(1,df$year)
}

## Calculate autocrrelation and durbinWatsontest for the linear model

library(car)

## Loading required package: carData

for (i in team_name){
  cat(paste("Team: ",i))
  cat("\n")
  #Construct the linear model
  cur_model=lm(df[,i]~df[,"year"])
  # formating
  print(durbinWatsonTest(cur_model))
  cat("\n")
  cat("\n")
}

## Team:  Orlando.Magic
##  lag Autocorrelation D-W Statistic p-value
##    1       0.7078625      0.581168       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Atlanta.Hawks
##  lag Autocorrelation D-W Statistic p-value
##    1       0.6832184     0.6229795       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Brooklyn.Nets
##  lag Autocorrelation D-W Statistic p-value
##    1       0.4444372     0.8767611       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Toronto.Raptors
##  lag Autocorrelation D-W Statistic p-value
##    1       0.5082855     0.8085398       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  New.York.Knicks
##  lag Autocorrelation D-W Statistic p-value
##    1       0.3163093      1.187897    0.02
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Dallas.Mavericks
##  lag Autocorrelation D-W Statistic p-value
##    1       0.3304898      1.163481   0.018
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Houston.Rockets
##  lag Autocorrelation D-W Statistic p-value
##    1       0.1085938      1.329416    0.06
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  San.Antonio.Spurs
##  lag Autocorrelation D-W Statistic p-value
##    1       0.6529772     0.5509981       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Chicago.Bulls
##  lag Autocorrelation D-W Statistic p-value
##    1       0.7297002     0.3983664       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Utah.Jazz
##  lag Autocorrelation D-W Statistic p-value
##    1         0.55544     0.7217189   0.002
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Portland.Trailblazers
##  lag Autocorrelation D-W Statistic p-value
##    1       0.5259033     0.8019058       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Golden.State.Warriors
##  lag Autocorrelation D-W Statistic p-value
##    1       0.6095012     0.6132759       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Memphis.Grizzlies
##  lag Autocorrelation D-W Statistic p-value
##    1       0.6370672     0.7025395       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Philadelphia.76ers
##  lag Autocorrelation D-W Statistic p-value
##    1        0.654117     0.5185056       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Boston.Celtics
##  lag Autocorrelation D-W Statistic p-value
##    1       0.4408933      1.093947   0.002
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Cleveland.Cavaliers
##  lag Autocorrelation D-W Statistic p-value
##    1       0.5886311     0.7720176       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Charlotte.Hornets
##  lag Autocorrelation D-W Statistic p-value
##    1       0.4752125     0.8775541   0.002
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Miami.Heat
##  lag Autocorrelation D-W Statistic p-value
##    1       0.4750486      1.021841   0.012
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Oklahoma.City.Thunder
##  lag Autocorrelation D-W Statistic p-value
##    1       0.5584059     0.7497431       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Los.Angeles.Lakers
##  lag Autocorrelation D-W Statistic p-value
##    1       0.7069464     0.4759136       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Denver.Nuggets
##  lag Autocorrelation D-W Statistic p-value
##    1       0.6666633     0.6630547       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Phoenix.Suns
##  lag Autocorrelation D-W Statistic p-value
##    1       0.4045231     0.9464731   0.006
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Los.Angeles.Clippers
##  lag Autocorrelation D-W Statistic p-value
##    1       0.5917471     0.8028749       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Washington.Wizards
##  lag Autocorrelation D-W Statistic p-value
##    1       0.5851073     0.7680514   0.002
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Detroit.Pistons
##  lag Autocorrelation D-W Statistic p-value
##    1       0.6492766     0.5486223       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Indiana.Pacers
##  lag Autocorrelation D-W Statistic p-value
##    1       0.4859199      1.015781   0.012
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Minnesota.Timberwolves
##  lag Autocorrelation D-W Statistic p-value
##    1       0.6335969     0.7228651       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Milwaukee.Bucks
##  lag Autocorrelation D-W Statistic p-value
##    1       0.5960961     0.6605117       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Sacramento.Kings
##  lag Autocorrelation D-W Statistic p-value
##    1        0.790246     0.3386508       0
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  New.Orleans.Pelicans
##  lag Autocorrelation D-W Statistic p-value
##    1        0.254611      1.455674   0.136
##  Alternative hypothesis: rho != 0

Get optimal order of autoregressive model

library(car)
# Create a list to store the optimal order
opt_order=list()
for(i in team_name){
  # Construct the autoregressive model
  model_time=ar.ols(df[,i],order.max = 9, demean = F, intercept = T)
  # formating
  cat(paste("\nTeam: ",i),"\n")
  cat("\n")
  print(model_time)
  cat("\n")
  cat("\n")
  # store the order into list
 opt_order=append(opt_order,model_time$order)
  
}

## 
## Team:  Orlando.Magic 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
##  1.2610  -0.3175  -0.1058   0.8743   0.3506  -0.6165   0.4616   0.3090  
##       9  
##  0.9459  
## 
## Intercept: -3291 (1748) 
## 
## Order selected 9  sigma^2 estimated as  1766
## 
## 
## 
## Team:  Atlanta.Hawks 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
##  0.2218   0.1476  -0.4475  -0.1623  -0.0099   0.5228  -0.6158   0.2043  
##       9  
## -0.5410  
## 
## Intercept: 2481 (442.1) 
## 
## Order selected 9  sigma^2 estimated as  912
## 
## 
## 
## Team:  Brooklyn.Nets 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
## -0.7649  -0.3135  -0.5825  -0.6694  -0.6194  -0.0945   0.3299   0.0618  
##       9  
## -0.5136  
## 
## Intercept: 5879 (805.6) 
## 
## Order selected 9  sigma^2 estimated as  526.1
## 
## 
## 
## Team:  Toronto.Raptors 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3  
##  0.8775  -0.0234  -0.1993  
## 
## Intercept: 521.3 (252.3) 
## 
## Order selected 3  sigma^2 estimated as  3439
## 
## 
## 
## Team:  New.York.Knicks 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7  
##  0.2437  -0.4389  -0.4524   0.0601  -0.2215  -0.5193  -0.5942  
## 
## Intercept: 4167 (710.1) 
## 
## Order selected 7  sigma^2 estimated as  1401
## 
## 
## 
## Team:  Dallas.Mavericks 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5  
##  1.0729  -0.8805   0.4968   0.2662  -0.0231  
## 
## Intercept: 85.29 (319.4) 
## 
## Order selected 5  sigma^2 estimated as  1568
## 
## 
## 
## Team:  Houston.Rockets 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6  
##  0.3829  -0.3951  -0.0897  -0.6887   0.7449  -0.7839  
## 
## Intercept: 2875 (742.3) 
## 
## Order selected 6  sigma^2 estimated as  2253
## 
## 
## 
## Team:  San.Antonio.Spurs 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4  
##  0.8795  -0.2906   0.0830  -0.8105  
## 
## Intercept: 1898 (628) 
## 
## Order selected 4  sigma^2 estimated as  1360
## 
## 
## 
## Team:  Chicago.Bulls 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
##  1.0809  -0.5619   0.3369  -0.2825   0.1049   0.0185  -0.6465   0.2785  
## 
## Intercept: 1010 (394.6) 
## 
## Order selected 8  sigma^2 estimated as  1701
## 
## 
## 
## Team:  Utah.Jazz 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
##  0.2328  -0.2364  -0.1576  -0.2025  -0.4816   0.0339  -0.7020   0.1963  
## 
## Intercept: 3546 (1148) 
## 
## Order selected 8  sigma^2 estimated as  845
## 
## 
## 
## Team:  Portland.Trailblazers 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
## -0.1902  -0.6522  -0.0369   0.0602   0.1058  -0.2094   0.4272   0.0097  
##       9  
## -0.1045  
## 
## Intercept: 2476 (618.2) 
## 
## Order selected 9  sigma^2 estimated as  559.2
## 
## 
## 
## Team:  Golden.State.Warriors 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
##  0.4948   0.4338   0.0332  -0.5788  -0.0925  -0.1548   0.2395   0.9725  
## 
## Intercept: -433.3 (372) 
## 
## Order selected 8  sigma^2 estimated as  1944
## 
## 
## 
## Team:  Memphis.Grizzlies 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
##  0.2244   0.5259  -0.4781  -0.6063   0.2779   0.1321  -0.1747  -0.3895  
##       9  
##  0.5808  
## 
## Intercept: 1399 (15.46) 
## 
## Order selected 9  sigma^2 estimated as  0.7429
## 
## 
## 
## Team:  Philadelphia.76ers 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
##  1.3727  -1.5085   0.9408  -0.9177   0.1059   0.2476  -0.5599   0.6490  
##       9  
##  0.3165  
## 
## Intercept: 465.1 (546.7) 
## 
## Order selected 9  sigma^2 estimated as  828.4
## 
## 
## 
## Team:  Boston.Celtics 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7  
##  0.0071  -0.4211  -0.0075  -0.4380  -0.2072  -0.5501   0.0328  
## 
## Intercept: 4017 (407.9) 
## 
## Order selected 7  sigma^2 estimated as  669.2
## 
## 
## 
## Team:  Cleveland.Cavaliers 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
##  0.3361  -0.6242  -0.2406  -0.7476  -0.2722  -0.2299  -0.3262   0.1527  
##       9  
## -0.4456  
## 
## Intercept: 5112 (1603) 
## 
## Order selected 9  sigma^2 estimated as  2646
## 
## 
## 
## Team:  Charlotte.Hornets 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2  
##  0.6590  -0.4131  
## 
## Intercept: 1072 (269.2) 
## 
## Order selected 2  sigma^2 estimated as  3134
## 
## 
## 
## Team:  Miami.Heat 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
## -0.0955   0.1991  -0.4512  -0.0397  -0.4760  -0.3900   0.2905  -0.3326  
##       9  
## -0.2339  
## 
## Intercept: 3953 (682) 
## 
## Order selected 9  sigma^2 estimated as  459.8
## 
## 
## 
## Team:  Oklahoma.City.Thunder 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
## -0.2071   0.3221   0.0814  -0.3042  -0.5986   0.4257   0.0392  -0.4389  
##       9  
## -0.0793  
## 
## Intercept: 2766 (248) 
## 
## Order selected 9  sigma^2 estimated as  418.8
## 
## 
## 
## Team:  Los.Angeles.Lakers 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
##  0.1666   0.6637   0.0488  -0.6747   0.0370   0.1771  -0.5461   0.2466  
##       9  
##  0.4365  
## 
## Intercept: 627.5 (238.9) 
## 
## Order selected 9  sigma^2 estimated as  344.4
## 
## 
## 
## Team:  Denver.Nuggets 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5  
##  1.0182  -0.5624   0.0248   0.1845  -0.3073  
## 
## Intercept: 990.7 (304.3) 
## 
## Order selected 5  sigma^2 estimated as  1193
## 
## 
## 
## Team:  Phoenix.Suns 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##      1  
## 0.6631  
## 
## Intercept: 509.2 (258.9) 
## 
## Order selected 1  sigma^2 estimated as  7621
## 
## 
## 
## Team:  Los.Angeles.Clippers 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
##  0.4756   0.3389  -0.0355  -0.3893  -0.0447   0.2167   0.2598  -0.1615  
##       9  
##  0.1127  
## 
## Intercept: 399.8 (285.8) 
## 
## Order selected 9  sigma^2 estimated as  788.1
## 
## 
## 
## Team:  Washington.Wizards 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
##  0.8659  -0.5565   0.2669  -0.3712  -0.5637  -0.0930   0.3938  -0.4912  
##       9  
## -0.2768  
## 
## Intercept: 2614 (537.3) 
## 
## Order selected 9  sigma^2 estimated as  99.77
## 
## 
## 
## Team:  Detroit.Pistons 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
##  0.7351  -0.3741   0.3139  -0.2870   0.1826  -0.3727   0.1043   0.1706  
## 
## Intercept: 743.8 (263.8) 
## 
## Order selected 8  sigma^2 estimated as  665.4
## 
## 
## 
## Team:  Indiana.Pacers 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4  
##  0.3621   0.1419  -0.2554  -0.2929  
## 
## Intercept: 1580 (404.4) 
## 
## Order selected 4  sigma^2 estimated as  1618
## 
## 
## 
## Team:  Minnesota.Timberwolves 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
##  0.4183   0.0294  -1.3940   0.9422   0.0671  -1.0643  -0.2245   1.6322  
##       9  
## -1.3629  
## 
## Intercept: 2780 (602.7) 
## 
## Order selected 9  sigma^2 estimated as  377.1
## 
## 
## 
## Team:  Milwaukee.Bucks 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##      1  
## 0.6983  
## 
## Intercept: 449.6 (253.3) 
## 
## Order selected 1  sigma^2 estimated as  4772
## 
## 
## 
## Team:  Sacramento.Kings 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
## -0.0177   0.0470  -0.5020   0.1371   0.1307  -0.6452   0.5042   0.0634  
##       9  
## -0.3674  
## 
## Intercept: 2329 (600.8) 
## 
## Order selected 9  sigma^2 estimated as  405.3
## 
## 
## 
## Team:  New.Orleans.Pelicans 
## 
## 
## Call:
## ar.ols(x = df[, i], order.max = 9, demean = F, intercept = T)
## 
## Coefficients:
##       1        2        3        4        5        6        7        8  
## -0.4686  -0.3205  -0.2445  -0.0419  -0.5930  -0.5498   0.1190  -0.2052  
##       9  
## -0.4513  
## 
## Intercept: 5534 (368.9) 
## 
## Order selected 9  sigma^2 estimated as  44.62

Durbin-Watson test statistic and model

library("tidyverse")

## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ tibble  3.1.8     ✔ dplyr   1.0.9
## ✔ tidyr   1.2.0     ✔ stringr 1.4.1
## ✔ readr   2.1.2     ✔ forcats 0.5.2
## ✔ purrr   0.3.4     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ✖ dplyr::recode() masks car::recode()
## ✖ purrr::some()   masks car::some()

# create a list to store the prediction for the next year average elo ratings
predict_result=list()

#index for the optimal order list
count=1
# loop to go over each team
for(i in team_name){
  
  # create a list to store the each lag column like lag1, lag2...
  group=list()
  
  # each team's elo ratings dataframe
  current_team=df[i]
  
  # optimal order
  counter<-opt_order[[count]]
 
  # create lag column based on the optimal order
  for(j in 1:counter){
    # create the lag column using dplyr
    current_team<-current_team %>%
    dplyr::mutate("lag{j}":=lag(df[,i],n=j,default=NA))
    
    # construct the lag column name string for later use and store it in the group list
    temp=paste("lag",j,sep = "")
    group=append(group,temp)
  }
  # go to the next optimal order for the next team
  count=count+1

 # construct the model formula to general model
  mymodel<-as.formula(paste(i,paste(group,collapse = "+"),sep = "~"))


 # use model lm function and model formula to generate the model
  current_model=lm(mymodel,data=current_team)
  # formmating
  cat(paste("Team: ",i))

  cat("\n")
  # print the summary of the model
  print(summary(current_model))
  
  # get the prediction for the next year elo ratings 
  prediction=tail(current_team,n=1)

  cat("The prediction for 2021 is the following\n")
  # output the predicted next year elo ratings
  print(predict(current_model,prediction))
  # store the predicted result into list
  predict_result=append(predict_result,predict(current_model,prediction))

  cat("\n")
  # run the durbinwatsonTest
  print(durbinWatsonTest(current_model))




cat("\n")
cat("\n")

}

## Team:  Orlando.Magic
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##      10      11      12      13      14      15      16      17      18      19 
##  43.086  69.914 -32.955 -89.378  27.115  37.724  21.766 -44.748 -16.437   3.135 
##      20      21 
## -21.363   2.142 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3290.9290  4282.0434  -0.769    0.523
## lag1            1.2610     0.6431   1.961    0.189
## lag2           -0.3175     0.9162  -0.347    0.762
## lag3           -0.1058     0.9095  -0.116    0.918
## lag4            0.8743     1.0467   0.835    0.491
## lag5            0.3506     1.3237   0.265    0.816
## lag6           -0.6165     0.8770  -0.703    0.555
## lag7            0.4616     0.7373   0.626    0.595
## lag8            0.3090     0.8620   0.358    0.754
## lag9            0.9459     1.2936   0.731    0.541
## 
## Residual standard error: 102.9 on 2 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.8621, Adjusted R-squared:  0.2418 
## F-statistic:  1.39 on 9 and 2 DF,  p-value: 0.487
## 
## The prediction for 2021 is the following
##       21 
## 1390.071 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1       0.1260496      1.660095   0.306
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Atlanta.Hawks
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##      10      11      12      13      14      15      16      17      18      19 
##  -8.293   8.195   9.461  19.820 -74.501  50.263  20.562   3.956 -36.026  11.919 
##      20      21 
##  10.669 -16.025 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept)  2.481e+03  1.083e+03   2.291    0.149
## lag1         2.218e-01  5.297e-01   0.419    0.716
## lag2         1.476e-01  6.392e-01   0.231    0.839
## lag3        -4.475e-01  5.066e-01  -0.883    0.470
## lag4        -1.623e-01  8.688e-01  -0.187    0.869
## lag5        -9.941e-03  6.785e-01  -0.015    0.990
## lag6         5.228e-01  4.542e-01   1.151    0.369
## lag7        -6.158e-01  8.803e-01  -0.700    0.557
## lag8         2.043e-01  1.548e+00   0.132    0.907
## lag9        -5.410e-01  1.084e+00  -0.499    0.667
## 
## Residual standard error: 73.97 on 2 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.8818, Adjusted R-squared:  0.3501 
## F-statistic: 1.658 on 9 and 2 DF,  p-value: 0.4321
## 
## The prediction for 2021 is the following
##       21 
## 1521.971 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.4134718      2.797194   0.644
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Brooklyn.Nets
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##        10        11        12        13        14        15        16        17 
##   9.45887  -5.16918  -9.47917  -0.00906   1.70910  24.50993 -13.77624 -33.76094 
##        18        19        20        21 
##  37.81599   9.09800 -45.22329  24.82601 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 5879.20147 1973.19697   2.980   0.0966 .
## lag1          -0.76487    0.60714  -1.260   0.3348  
## lag2          -0.31346    0.58533  -0.536   0.6459  
## lag3          -0.58246    0.43639  -1.335   0.3136  
## lag4          -0.66939    0.53270  -1.257   0.3358  
## lag5          -0.61944    0.60822  -1.018   0.4156  
## lag6          -0.09449    0.51676  -0.183   0.8718  
## lag7           0.32987    0.40974   0.805   0.5053  
## lag8           0.06185    0.35770   0.173   0.8786  
## lag9          -0.51355    0.31472  -1.632   0.2443  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 56.19 on 2 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.9359, Adjusted R-squared:  0.6473 
## F-statistic: 3.243 on 9 and 2 DF,  p-value: 0.2579
## 
## The prediction for 2021 is the following
##       21 
## 1554.036 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.3638659      2.615941   0.592
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Toronto.Raptors
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -109.33  -30.75   12.38   41.02   83.08 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 521.32031  286.07583   1.822  0.08983 . 
## lag1          0.87755    0.25440   3.450  0.00391 **
## lag2         -0.02344    0.35904  -0.065  0.94888   
## lag3         -0.19932    0.28243  -0.706  0.49193   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 66.49 on 14 degrees of freedom
##   (3 observations deleted due to missingness)
## Multiple R-squared:  0.6588, Adjusted R-squared:  0.5857 
## F-statistic: 9.011 on 3 and 14 DF,  p-value: 0.001416
## 
## The prediction for 2021 is the following
##       21 
## 1628.819 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1     -0.01541888      1.868053   0.568
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  New.York.Knicks
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -63.320 -13.610  -1.604  17.710  81.321 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 4166.90433 1084.72628   3.841  0.00854 **
## lag1           0.24370    0.29564   0.824  0.44130   
## lag2          -0.43890    0.32414  -1.354  0.22450   
## lag3          -0.45238    0.32738  -1.382  0.21628   
## lag4           0.06009    0.33736   0.178  0.86449   
## lag5          -0.22152    0.33195  -0.667  0.52937   
## lag6          -0.51931    0.33107  -1.569  0.16780   
## lag7          -0.59425    0.33553  -1.771  0.12694   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 57.18 on 6 degrees of freedom
##   (7 observations deleted due to missingness)
## Multiple R-squared:  0.7636, Adjusted R-squared:  0.4879 
## F-statistic: 2.769 on 7 and 6 DF,  p-value: 0.1177
## 
## The prediction for 2021 is the following
##       21 
## 1479.568 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.1293712      2.247181   0.926
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Dallas.Mavericks
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -52.839 -24.192  -5.515  14.407  83.610 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  85.29450  404.03740   0.211  0.83704   
## lag1          1.07295    0.26939   3.983  0.00259 **
## lag2         -0.88049    0.39620  -2.222  0.05050 . 
## lag3          0.49677    0.41936   1.185  0.26356   
## lag4          0.26618    0.37030   0.719  0.48870   
## lag5         -0.02313    0.38972  -0.059  0.95385   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 50.09 on 10 degrees of freedom
##   (5 observations deleted due to missingness)
## Multiple R-squared:  0.7866, Adjusted R-squared:  0.6798 
## F-statistic:  7.37 on 5 and 10 DF,  p-value: 0.003875
## 
## The prediction for 2021 is the following
##       21 
## 1537.109 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.1438985      2.246477   0.922
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Houston.Rockets
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -66.470 -40.707   8.202  35.983 112.950 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 2874.86313 1016.48613   2.828   0.0222 *
## lag1           0.38293    0.38574   0.993   0.3499  
## lag2          -0.39509    0.46644  -0.847   0.4216  
## lag3          -0.08973    0.49966  -0.180   0.8619  
## lag4          -0.68869    0.59113  -1.165   0.2776  
## lag5           0.74495    0.48896   1.524   0.1661  
## lag6          -0.78395    0.42491  -1.845   0.1023  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 64.99 on 8 degrees of freedom
##   (6 observations deleted due to missingness)
## Multiple R-squared:  0.5266, Adjusted R-squared:  0.1716 
## F-statistic: 1.483 on 6 and 8 DF,  p-value: 0.2953
## 
## The prediction for 2021 is the following
##       21 
## 1453.666 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      0.05963411      1.744307   0.404
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  San.Antonio.Spurs
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -62.496 -25.699  -3.759  12.931  77.660 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 1897.89288  747.43059   2.539  0.02598 * 
## lag1           0.87953    0.24733   3.556  0.00395 **
## lag2          -0.29057    0.35733  -0.813  0.43196   
## lag3           0.08296    0.35409   0.234  0.81871   
## lag4          -0.81052    0.37615  -2.155  0.05219 . 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 43.9 on 12 degrees of freedom
##   (4 observations deleted due to missingness)
## Multiple R-squared:  0.7504, Adjusted R-squared:  0.6671 
## F-statistic: 9.017 on 4 and 12 DF,  p-value: 0.001332
## 
## The prediction for 2021 is the following
##       21 
## 1510.932 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1     0.008788928      1.906495   0.608
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Chicago.Bulls
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##       9      10      11      12      13      14      15      16      17      18 
## -26.985 -50.137  93.793  38.838 -52.155  59.184  11.774 -44.477  -6.178 -10.167 
##      19      20      21 
##  -3.704  -8.636  -1.151 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 1009.99713  711.36149   1.420   0.2287  
## lag1           1.08087    0.38144   2.834   0.0472 *
## lag2          -0.56190    0.46940  -1.197   0.2974  
## lag3           0.33691    0.53390   0.631   0.5623  
## lag4          -0.28254    0.53264  -0.530   0.6239  
## lag5           0.10485    0.44169   0.237   0.8240  
## lag6           0.01854    0.46693   0.040   0.9702  
## lag7          -0.64652    0.48053  -1.345   0.2497  
## lag8           0.27852    0.37601   0.741   0.5000  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 74.36 on 4 degrees of freedom
##   (8 observations deleted due to missingness)
## Multiple R-squared:  0.8218, Adjusted R-squared:  0.4655 
## F-statistic: 2.306 on 8 and 4 DF,  p-value: 0.2188
## 
## The prediction for 2021 is the following
##       21 
## 1427.732 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.1911908      2.349398   0.602
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Utah.Jazz
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##       9      10      11      12      13      14      15      16      17      18 
##  10.613  35.174 -37.461 -31.698  24.178 -28.159   7.206  -1.536  27.261 -33.596 
##      19      20      21 
## -36.864  17.282  47.600 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3546.11609 2069.02078   1.714    0.162
## lag1           0.23275    0.48364   0.481    0.655
## lag2          -0.23644    0.45628  -0.518    0.632
## lag3          -0.15759    0.48068  -0.328    0.759
## lag4          -0.20252    0.46852  -0.432    0.688
## lag5          -0.48159    0.50128  -0.961    0.391
## lag6           0.03393    0.46183   0.073    0.945
## lag7          -0.70202    0.41187  -1.704    0.163
## lag8           0.19628    0.40905   0.480    0.656
## 
## Residual standard error: 52.4 on 4 degrees of freedom
##   (8 observations deleted due to missingness)
## Multiple R-squared:  0.8127, Adjusted R-squared:  0.438 
## F-statistic: 2.169 on 8 and 4 DF,  p-value: 0.237
## 
## The prediction for 2021 is the following
##       21 
## 1598.861 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1     -0.08664652       1.95678   0.578
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Portland.Trailblazers
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##      10      11      12      13      14      15      16      17      18      19 
## -24.239  32.062  18.404 -57.122  27.390   8.374 -12.573  -8.889  -8.263  16.620 
##      20      21 
##   9.453  -1.217 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept)  2.476e+03  1.514e+03   1.635    0.244
## lag1        -1.902e-01  6.571e-01  -0.290    0.799
## lag2        -6.522e-01  4.416e-01  -1.477    0.278
## lag3        -3.685e-02  5.901e-01  -0.062    0.956
## lag4         6.018e-02  4.950e-01   0.122    0.914
## lag5         1.058e-01  4.786e-01   0.221    0.846
## lag6        -2.094e-01  4.940e-01  -0.424    0.713
## lag7         4.272e-01  4.959e-01   0.862    0.480
## lag8         9.713e-03  5.951e-01   0.016    0.988
## lag9        -1.045e-01  3.748e-01  -0.279    0.807
## 
## Residual standard error: 57.92 on 2 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.712,  Adjusted R-squared:  -0.5841 
## F-statistic: 0.5493 on 9 and 2 DF,  p-value: 0.7832
## 
## The prediction for 2021 is the following
##       21 
## 1527.184 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.3704038      2.653024    0.58
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Golden.State.Warriors
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##       9      10      11      12      13      14      15      16      17      18 
## -11.828 -49.272 -24.610  43.017  39.640  -5.591  19.327 -44.516   4.074  32.786 
##      19      20      21 
##  75.693 -95.775  17.055 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -433.33847  670.54649  -0.646    0.553
## lag1           0.49477    0.37997   1.302    0.263
## lag2           0.43384    0.52799   0.822    0.457
## lag3           0.03316    0.52136   0.064    0.952
## lag4          -0.57875    0.49947  -1.159    0.311
## lag5          -0.09252    0.48631  -0.190    0.858
## lag6          -0.15482    0.52731  -0.294    0.784
## lag7           0.23949    0.53850   0.445    0.680
## lag8           0.97248    0.47930   2.029    0.112
## 
## Residual standard error: 79.48 on 4 degrees of freedom
##   (8 observations deleted due to missingness)
## Multiple R-squared:  0.9122, Adjusted R-squared:  0.7365 
## F-statistic: 5.192 on 8 and 4 DF,  p-value: 0.06448
## 
## The prediction for 2021 is the following
##       21 
## 1446.276 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.2056957      2.394342    0.82
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Memphis.Grizzlies
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##       10       11       12       13       14       15       16       17 
##  0.12159 -0.88427  1.16064 -0.16331 -0.35559 -0.34525  1.05033  0.08741 
##       18       19       20       21 
## -1.22601  0.05672  1.61950 -1.12177 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1398.65662   37.87402  36.929 0.000732 ***
## lag1           0.22436    0.02098  10.695 0.008629 ** 
## lag2           0.52586    0.02322  22.647 0.001944 ** 
## lag3          -0.47810    0.02635 -18.146 0.003023 ** 
## lag4          -0.60634    0.03405 -17.806 0.003139 ** 
## lag5           0.27788    0.02906   9.561 0.010763 *  
## lag6           0.13213    0.03271   4.040 0.056162 .  
## lag7          -0.17474    0.02308  -7.570 0.017007 *  
## lag8          -0.38954    0.02556 -15.238 0.004279 ** 
## lag9           0.58084    0.02007  28.936 0.001192 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.111 on 2 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.9999, Adjusted R-squared:  0.9992 
## F-statistic:  1620 on 9 and 2 DF,  p-value: 0.0006169
## 
## The prediction for 2021 is the following
##       21 
## 1528.324 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.3718603      2.600901   0.676
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Philadelphia.76ers
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##       10       11       12       13       14       15       16       17 
## -31.6444  56.6754 -13.3048  44.9596 -51.8601  16.8540 -19.0703  -4.1119 
##       18       19       20       21 
##  11.4159  -5.6791  -0.9383  -3.2960 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)  465.1192  1339.2229   0.347    0.762
## lag1           1.3727     0.5185   2.648    0.118
## lag2          -1.5085     0.8294  -1.819    0.211
## lag3           0.9408     1.0625   0.886    0.469
## lag4          -0.9177     1.1483  -0.799    0.508
## lag5           0.1059     1.2331   0.086    0.939
## lag6           0.2476     1.2089   0.205    0.857
## lag7          -0.5599     0.9581  -0.584    0.618
## lag8           0.6490     0.9878   0.657    0.579
## lag9           0.3165     0.5151   0.614    0.602
## 
## Residual standard error: 70.5 on 2 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.9498, Adjusted R-squared:  0.7241 
## F-statistic: 4.208 on 9 and 2 DF,  p-value: 0.2067
## 
## The prediction for 2021 is the following
##       21 
## 1600.888 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.6737935      3.245756    0.63
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Boston.Celtics
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -59.627  -7.712   3.388  15.393  48.284 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  4.017e+03  6.231e+02   6.446  0.00066 ***
## lag1         7.110e-03  1.658e-01   0.043  0.96719    
## lag2        -4.211e-01  1.688e-01  -2.495  0.04684 *  
## lag3        -7.518e-03  1.903e-01  -0.040  0.96977    
## lag4        -4.380e-01  1.652e-01  -2.652  0.03793 *  
## lag5        -2.072e-01  1.784e-01  -1.161  0.28959    
## lag6        -5.501e-01  1.734e-01  -3.172  0.01928 *  
## lag7         3.276e-02  1.586e-01   0.207  0.84319    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 39.52 on 6 degrees of freedom
##   (7 observations deleted due to missingness)
## Multiple R-squared:  0.9051, Adjusted R-squared:  0.7944 
## F-statistic: 8.176 on 7 and 6 DF,  p-value: 0.01026
## 
## The prediction for 2021 is the following
##       21 
## 1599.358 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1       0.1518778      1.490741   0.294
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Cleveland.Cavaliers
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##      10      11      12      13      14      15      16      17      18      19 
## 106.516 -75.357  65.752 -18.947  46.459  -2.458  23.623 -40.379 -16.263   7.556 
##      20      21 
## -29.321 -67.181 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5112.0209  3926.7469   1.302    0.323
## lag1           0.3361     0.5533   0.607    0.605
## lag2          -0.6242     0.4884  -1.278    0.330
## lag3          -0.2406     0.6843  -0.352    0.759
## lag4          -0.7476     0.5763  -1.297    0.324
## lag5          -0.2722     0.7882  -0.345    0.763
## lag6          -0.2299     0.5975  -0.385    0.738
## lag7          -0.3262     0.6203  -0.526    0.651
## lag8           0.1527     0.5311   0.288    0.801
## lag9          -0.4456     0.4882  -0.913    0.458
## 
## Residual standard error: 126 on 2 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.8734, Adjusted R-squared:  0.3036 
## F-statistic: 1.533 on 9 and 2 DF,  p-value: 0.4562
## 
## The prediction for 2021 is the following
##       21 
## 1428.026 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.4393673      2.379305   0.886
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Charlotte.Hornets
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -127.020  -44.501    4.702   55.194   73.284 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 1072.0092   293.3040   3.655  0.00214 **
## lag1           0.6590     0.2224   2.963  0.00916 **
## lag2          -0.4131     0.2017  -2.048  0.05739 . 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 61.01 on 16 degrees of freedom
##   (2 observations deleted due to missingness)
## Multiple R-squared:  0.3621, Adjusted R-squared:  0.2823 
## F-statistic: 4.541 on 2 and 16 DF,  p-value: 0.02743
## 
## The prediction for 2021 is the following
##       21 
## 1383.525 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1     -0.02894974      1.962441   0.752
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Miami.Heat
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##      10      11      12      13      14      15      16      17      18      19 
## -12.459  26.631 -13.723 -17.586  45.572 -23.775  -5.936  17.536 -16.960   6.690 
##      20      21 
##  17.259 -23.248 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3953.30818 1670.63252   2.366    0.142
## lag1          -0.09548    0.62626  -0.152    0.893
## lag2           0.19911    0.39078   0.510    0.661
## lag3          -0.45117    0.28055  -1.608    0.249
## lag4          -0.03965    0.39720  -0.100    0.930
## lag5          -0.47604    0.33883  -1.405    0.295
## lag6          -0.39000    0.40016  -0.975    0.433
## lag7           0.29047    0.31832   0.913    0.458
## lag8          -0.33257    0.41366  -0.804    0.506
## lag9          -0.23388    0.39612  -0.590    0.615
## 
## Residual standard error: 52.52 on 2 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.9301, Adjusted R-squared:  0.6157 
## F-statistic: 2.958 on 9 and 2 DF,  p-value: 0.2781
## 
## The prediction for 2021 is the following
##       21 
## 1560.261 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.5437965      2.961501   0.478
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Oklahoma.City.Thunder
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##      10      11      12      13      14      15      16      17      18      19 
##  -3.343  -1.018  19.622 -16.791 -11.618  26.673  -0.207 -14.547 -13.400  21.903 
##      20      21 
##  32.434 -39.708 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 2765.64610  607.57177   4.552    0.045 *
## lag1          -0.20709    0.31352  -0.661    0.577  
## lag2           0.32214    0.29646   1.087    0.391  
## lag3           0.08138    0.26817   0.303    0.790  
## lag4          -0.30423    0.27355  -1.112    0.382  
## lag5          -0.59861    0.30271  -1.978    0.187  
## lag6           0.42568    0.24042   1.771    0.219  
## lag7           0.03919    0.26162   0.150    0.895  
## lag8          -0.43891    0.25309  -1.734    0.225  
## lag9          -0.07933    0.23543  -0.337    0.768  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 50.13 on 2 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.9241, Adjusted R-squared:  0.5825 
## F-statistic: 2.705 on 9 and 2 DF,  p-value: 0.299
## 
## The prediction for 2021 is the following
##      21 
## 1465.17 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.2267425        2.1375   0.844
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Los.Angeles.Lakers
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##      10      11      12      13      14      15      16      17      18      19 
##  18.450 -17.816 -11.321  25.816 -20.411   3.817   6.565   2.730  -3.688 -29.192 
##      20      21 
##  35.093 -10.043 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) 627.45354  585.08022   1.072    0.396
## lag1          0.16657    0.38398   0.434    0.707
## lag2          0.66368    0.48623   1.365    0.306
## lag3          0.04880    0.57908   0.084    0.941
## lag4         -0.67473    0.50585  -1.334    0.314
## lag5          0.03705    0.55920   0.066    0.953
## lag6          0.17710    0.61046   0.290    0.799
## lag7         -0.54611    0.46542  -1.173    0.361
## lag8          0.24658    0.37409   0.659    0.578
## lag9          0.43650    0.39064   1.117    0.380
## 
## Residual standard error: 45.46 on 2 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.9805, Adjusted R-squared:  0.8926 
## F-statistic: 11.16 on 9 and 2 DF,  p-value: 0.0849
## 
## The prediction for 2021 is the following
##       21 
## 1629.771 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.5470077       2.98723    0.04
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Denver.Nuggets
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -90.587 -17.687  -4.533  23.024  67.624 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 990.68086  384.88584   2.574  0.02770 * 
## lag1          1.01817    0.27546   3.696  0.00413 **
## lag2         -0.56239    0.36279  -1.550  0.15214   
## lag3          0.02476    0.28639   0.086  0.93281   
## lag4          0.18452    0.26319   0.701  0.49923   
## lag5         -0.30728    0.19439  -1.581  0.14502   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 43.69 on 10 degrees of freedom
##   (5 observations deleted due to missingness)
## Multiple R-squared:  0.6956, Adjusted R-squared:  0.5434 
## F-statistic:  4.57 on 5 and 10 DF,  p-value: 0.0198
## 
## The prediction for 2021 is the following
##       21 
## 1589.593 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.1386837      2.249466     0.9
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Phoenix.Suns
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -151.253  -77.410   -8.986   55.595  183.052 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 509.1778   272.8555   1.866  0.07841 . 
## lag1          0.6631     0.1806   3.672  0.00175 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 92.02 on 18 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.4282, Adjusted R-squared:  0.3964 
## F-statistic: 13.48 on 1 and 18 DF,  p-value: 0.001746
## 
## The prediction for 2021 is the following
##       21 
## 1445.768 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1       0.1435297      1.477901   0.142
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Los.Angeles.Clippers
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##      10      11      12      13      14      15      16      17      18      19 
##  -3.181 -31.327  40.661   0.787 -20.714 -12.292  19.182  36.117 -24.687 -45.787 
##      20      21 
##  43.009  -1.768 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) 399.80509  700.17143   0.571    0.626
## lag1          0.47556    0.51880   0.917    0.456
## lag2          0.33891    0.64844   0.523    0.653
## lag3         -0.03547    0.62637  -0.057    0.960
## lag4         -0.38935    0.63691  -0.611    0.603
## lag5         -0.04467    0.65898  -0.068    0.952
## lag6          0.21674    0.62486   0.347    0.762
## lag7          0.25983    0.58662   0.443    0.701
## lag8         -0.16153    0.48663  -0.332    0.771
## lag9          0.11272    0.42446   0.266    0.815
## 
## Residual standard error: 68.76 on 2 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.9143, Adjusted R-squared:  0.5286 
## F-statistic:  2.37 on 9 and 2 DF,  p-value: 0.3318
## 
## The prediction for 2021 is the following
##       21 
## 1634.569 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.2382829      2.475166    0.75
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Washington.Wizards
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##       10       11       12       13       14       15       16       17 
##   0.5221   5.9482 -13.4071  -0.3220  11.1437   5.3452 -16.1152  10.1718 
##       18       19       20       21 
## -14.0155  14.7946   2.5594  -6.6252 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 2613.95670 1316.10112   1.986   0.1854  
## lag1           0.86593    0.26250   3.299   0.0809 .
## lag2          -0.55653    0.33951  -1.639   0.2428  
## lag3           0.26694    0.40086   0.666   0.5740  
## lag4          -0.37120    0.30510  -1.217   0.3478  
## lag5          -0.56374    0.36683  -1.537   0.2642  
## lag6          -0.09296    0.19922  -0.467   0.6867  
## lag7           0.39385    0.24721   1.593   0.2521  
## lag8          -0.49119    0.23119  -2.125   0.1676  
## lag9          -0.27685    0.29875  -0.927   0.4519  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 24.47 on 2 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.9856, Adjusted R-squared:  0.9208 
## F-statistic: 15.21 on 9 and 2 DF,  p-value: 0.0632
## 
## The prediction for 2021 is the following
##       21 
## 1418.868 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.4973467      2.957801   0.946
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Detroit.Pistons
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##       9      10      11      12      13      14      15      16      17      18 
##   4.692  -5.494  -8.677  27.502  10.099 -16.436 -28.473  36.445 -25.875  41.688 
##      19      20      21 
##  27.129 -22.583 -40.017 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 743.8335   475.6279   1.564   0.1929  
## lag1          0.7351     0.2837   2.591   0.0606 .
## lag2         -0.3741     0.3480  -1.075   0.3428  
## lag3          0.3139     0.2946   1.065   0.3467  
## lag4         -0.2870     0.2736  -1.049   0.3534  
## lag5          0.1826     0.2854   0.640   0.5570  
## lag6         -0.3727     0.3201  -1.164   0.3091  
## lag7          0.1043     0.3317   0.314   0.7689  
## lag8          0.1706     0.2635   0.647   0.5527  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 46.5 on 4 degrees of freedom
##   (8 observations deleted due to missingness)
## Multiple R-squared:  0.7852, Adjusted R-squared:  0.3557 
## F-statistic: 1.828 on 8 and 4 DF,  p-value: 0.2932
## 
## The prediction for 2021 is the following
##       21 
## 1401.877 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.1473349      2.106992   0.484
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Indiana.Pacers
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -89.603 -28.607  -1.564  36.577  54.630 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 1579.6909   481.3800   3.282  0.00656 **
## lag1           0.3621     0.2445   1.481  0.16434   
## lag2           0.1419     0.2616   0.542  0.59748   
## lag3          -0.2554     0.2603  -0.981  0.34598   
## lag4          -0.2929     0.2442  -1.199  0.25352   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 47.88 on 12 degrees of freedom
##   (4 observations deleted due to missingness)
## Multiple R-squared:  0.4788, Adjusted R-squared:  0.3051 
## F-statistic: 2.756 on 4 and 12 DF,  p-value: 0.07764
## 
## The prediction for 2021 is the following
##      21 
## 1536.01 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      0.07777077      1.801042   0.526
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Minnesota.Timberwolves
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##      10      11      12      13      14      15      16      17      18      19 
##  22.978 -37.183  -6.050  26.090  15.351 -36.063  13.106   2.456  -9.974   7.081 
##      20      21 
##   5.049  -2.842 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 2779.50199 1476.27590   1.883   0.2004  
## lag1           0.41826    0.32332   1.294   0.3250  
## lag2           0.02937    0.44606   0.066   0.9535  
## lag3          -1.39401    0.42551  -3.276   0.0819 .
## lag4           0.94217    0.58040   1.623   0.2460  
## lag5           0.06706    0.34713   0.193   0.8647  
## lag6          -1.06425    0.44976  -2.366   0.1416  
## lag7          -0.22445    0.36084  -0.622   0.5974  
## lag8           1.63223    0.84573   1.930   0.1934  
## lag9          -1.36294    0.45213  -3.014   0.0947 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 47.57 on 2 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.941,  Adjusted R-squared:  0.6757 
## F-statistic: 3.546 on 9 and 2 DF,  p-value: 0.2393
## 
## The prediction for 2021 is the following
##       21 
## 1337.113 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.3214432      2.524416   0.498
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Milwaukee.Bucks
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -178.289  -30.933   -4.362   27.501  158.328 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 449.6498   266.9548   1.684  0.10937   
## lag1          0.6983     0.1797   3.885  0.00108 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 72.82 on 18 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.4561, Adjusted R-squared:  0.4259 
## F-statistic: 15.09 on 1 and 18 DF,  p-value: 0.001085
## 
## The prediction for 2021 is the following
##       21 
## 1646.317 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1       0.0415015      1.910716   0.726
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  Sacramento.Kings
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##       10       11       12       13       14       15       16       17 
##  16.8227 -18.1093 -15.6240  12.6885  10.2927 -16.6762  24.5996   0.2709 
##       18       19       20       21 
## -45.5850  22.8941  14.7130  -6.2869 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2328.83270 1471.64082   1.582    0.254
## lag1          -0.01771    0.62149  -0.029    0.980
## lag2           0.04696    0.45687   0.103    0.928
## lag3          -0.50203    0.46120  -1.089    0.390
## lag4           0.13712    0.66529   0.206    0.856
## lag5           0.13065    0.61004   0.214    0.850
## lag6          -0.64522    0.59598  -1.083    0.392
## lag7           0.50420    0.65465   0.770    0.522
## lag8           0.06343    0.69507   0.091    0.936
## lag9          -0.36745    0.49821  -0.738    0.538
## 
## Residual standard error: 49.31 on 2 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.7678, Adjusted R-squared:  -0.2771 
## F-statistic: 0.7348 on 9 and 2 DF,  p-value: 0.6955
## 
## The prediction for 2021 is the following
##       21 
## 1446.737 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.3035296      2.540742   0.118
##  Alternative hypothesis: rho != 0
## 
## 
## Team:  New.Orleans.Pelicans
## 
## Call:
## lm(formula = mymodel, data = current_team)
## 
## Residuals:
##       10       11       12       13       14       15       16       17 
##  -1.7506   7.4906  -1.6415  -7.1924   7.1048   4.5666  -7.9146   1.2695 
##       18       19       20       21 
##  -0.1136   0.2161  10.9003 -12.9353 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept) 5533.93275  903.61367   6.124   0.0256 *
## lag1          -0.46855    0.21848  -2.145   0.1652  
## lag2          -0.32049    0.12173  -2.633   0.1190  
## lag3          -0.24454    0.17080  -1.432   0.2886  
## lag4          -0.04189    0.11133  -0.376   0.7429  
## lag5          -0.59298    0.12708  -4.666   0.0430 *
## lag6          -0.54979    0.10103  -5.442   0.0321 *
## lag7           0.11901    0.11520   1.033   0.4101  
## lag8          -0.20518    0.11236  -1.826   0.2094  
## lag9          -0.45129    0.14782  -3.053   0.0926 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.36 on 2 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.9753, Adjusted R-squared:  0.864 
## F-statistic: 8.766 on 9 and 2 DF,  p-value: 0.1065
## 
## The prediction for 2021 is the following
##       21 
## 1499.124 
## 
##  lag Autocorrelation D-W Statistic p-value
##    1      -0.4058042      2.493356   0.522
##  Alternative hypothesis: rho != 0

Get the prediction

# convert list to matrix
predict_result=do.call(rbind, predict_result)
# rename column name
colnames(predict_result)="Predict"
# add team name
predict_result=cbind(team_name,predict_result)

# convert matrix to dataframe
predict_result=as.data.frame(predict_result)
# remove row name
predict_result = predict_result %>% `rownames<-`( NULL )
predict_result

##                 team_name          Predict
## 1           Orlando.Magic 1390.07126942078
## 2           Atlanta.Hawks 1521.97140846065
## 3           Brooklyn.Nets 1554.03594903058
## 4         Toronto.Raptors 1628.81857631474
## 5         New.York.Knicks  1479.5675913124
## 6        Dallas.Mavericks 1537.10852982091
## 7         Houston.Rockets 1453.66626037168
## 8       San.Antonio.Spurs 1510.93176491456
## 9           Chicago.Bulls 1427.73213753544
## 10              Utah.Jazz 1598.86081444179
## 11  Portland.Trailblazers 1527.18381011028
## 12  Golden.State.Warriors 1446.27563367298
## 13      Memphis.Grizzlies 1528.32432086334
## 14     Philadelphia.76ers 1600.88776990946
## 15         Boston.Celtics 1599.35754871597
## 16    Cleveland.Cavaliers  1428.0258114195
## 17      Charlotte.Hornets 1383.52479413362
## 18             Miami.Heat 1560.26145216225
## 19  Oklahoma.City.Thunder 1465.16989285989
## 20     Los.Angeles.Lakers 1629.77056559193
## 21         Denver.Nuggets 1589.59252061288
## 22           Phoenix.Suns 1445.76839336782
## 23   Los.Angeles.Clippers 1634.56927947088
## 24     Washington.Wizards  1418.8684880605
## 25        Detroit.Pistons 1401.87711993017
## 26         Indiana.Pacers 1536.00965953525
## 27 Minnesota.Timberwolves 1337.11275427319
## 28        Milwaukee.Bucks 1646.31737219909
## 29       Sacramento.Kings 1446.73745745777
## 30   New.Orleans.Pelicans 1499.12426646209